Painting 2 x 4 studs

Should use a sealing primer, or a sealer first if they are pine or fir studs. Shellac any knotholes so they do not bleed through at the very least. You will need to paint the drywall before you paint it too.

Joe raises a good point about the fire code. On the living side of the furnace room you most certainly need 5/8. Perhaps not where you are on the side to the basement or whatever. Check code to be certain.